When Republican senator Thad Cochran celebrated victory in a closely watched Mississippi primary last night, it also marked a notable win for former mayor Michael Bloomberg.

Bloomberg has enjoyed only modest success in his effort to elect putative moderates from both parties, and he bet big on Cochran's chances in a tough run-off against an energetic Tea Party challenger.

The former mayor appears to have been Cochran's single biggest benefactor, with at least half a million dollars committed to the race.

He gave $250,000 to Cochran's super PAC, Mississippi Conservatives, and another $250,000 to Defending Main Street, a centrist-conservative super PAC that was also backing Cochran. (The Defending Main Street contribution was first reported by the New York Times, and confirmed to Capital by a spokesman for the mayor.)

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Bloomberg's efforts to keep his backing of moderates bipartisan frequently puts him in the odd position of supporting Republicans, like Cochran, who directly oppose him on the issues he cares most about.

In March, Cochran received the enthusiastic endorsement of the National Rifle Association, which cited his lifelong A+ rating and the fact he "stood strong against President Obama and former NY City Mayor Michael Bloomberg's gun control agenda."

But Cochran was also seen as a relatively pro-business Republican, who voted for increases in the debt ceiling and the minimum wage, which were opposed by Tea Party conservatives.

For Bloomberg, who has decried the Tea Party's influence in Washington, Cochran's win could be especially significant, coming after the defeat of House majority leader Eric Cantor in Virginia threatened to re-energize the flagging movement.

Cochran's opponent, state Senator Chris McDaniel, promised to be a conservative ally to U.S. senators like Ted Cruz and Mike Lee, who have loudly opposed Bloomberg's brand of governance, which is pro-business without being systematically anti-tax or anti-government.

McDaniel was backed by millions of dollars in outside spending from conservative groups who saw an opportunity to replace a aging mainstream Republican incumbent with a young hard-liner.

Bloomberg and other pro-business moderates, including former Napster founder Sean Parker, saw a path for Cochran, who eventually mobilized enough traditionally Democratic voters to edge out McDaniel in yesterday's run-off, to the consternation of McDaniel and his supporters.

That win makes Cantor's defeat look more like an anomaly in an election cycle in which conservative opponents did not fare well against pragmatic incumbents like Cochran.